Parametric Instability of Circular Cylindrical Shells

Abstract

Parametric instability of thin, circular cylindrical shells subjected to in-plane longitudinal inertia loading arising from sinusoidal base excitation has been investigated analytically and experimentally. The shell under consideration was rigidly clamped at the base and free at the upper edge. In the applied excitation frequency range, the test specimens exhibited lateral vibrations, at half the driving frequency, with one half longitudinal wave and three full circumferential waves. The linear bending theory used in the analysis was adequate in predicting the incipience of instability, just as in the case of slender rods. Attention has been confined to investigating only the principal instability region, as observed during the experiments. Excellent agreement was obtained between the analytical and experimental results.

Dynamic Stability Problems of Anisotropic Cylindrical Shells via a Simplified Analysis

“…The essential ideas for shell problems are discussed by Hsu [4]. The parametric excitation of cylindrical shells was studied by Yao, both in a linear and in a nonlinear context [5,6], and by Vijayaraghavan and Evan-Iwanowski [7]. Nagai and Yamaki [8] included the effect of boundary conditions and the effect of axisymmetric bending vibrations in the fundamental state in their analysis.…”

Dynamic stability analysis of cross-ply laminated cylindrical shells using different thin shell theories

“…The subject of parametric resonance in cylindrical shells under periodic loads has received much attention since it was first examined by Bolotin [1], Yao [2] and Vijayaraghavan and Evan-Iwanowski [3]. Bert and Birman [4], in one of the most extensive studies on this subject, extended Yao's [2] approach and studied the parametric instability of thick orthotropic shells using higher order shell theories.…”

Parametric Instability of Doubly Curved Panels Subjected to Non-Uniform Harmonic Loading

“…The parametric instability characteristics of plates subjected to uniform loads were studied by Hutt and Salam [2] using "nite element method. Parametric resonance in shell structures under periodic loads had been of considerable interest since the subject was studied by Bolotin [3], Yao [4], Bieniek et al [5] and Vijayaraghavan and Evan-Iwanowski [6]. The method of solution of these class of problems were to "rst reduce the equations of motion to a system of Mathieu}Hill equations and the parametric resonance characteristics were studied by di!erent methods.…”